The value of the 3 in 395,047 is
£10 times greater than the value of the
3 in which of these numbers
386592
283429
136258
123694

Hello there. To solve this question, we'll have to remember some properties about angles and the unit circle.

First, remember the unit circle:

An angle is represented as the measure between the line joining the origin and any point of the circle with the x-axis, as follows

The full angle in this case, representing a cycle in the circle is

So we want to determine all angles θ between 0 and 360º such that

For this, we have to remember about first positive determination of an angle.

Notice we can represent negative angles in the unit circle if, instead of following in the anti-clockwise orientation (we say positive orientation), we follow the other way around:

But notice that we can represent these angles with our first case if you consider:

Since you have the property that the full angles is 2pi, hence

Thefore you have that

In this case notice that we added 360º to the angle, since we fixed the point of which the angle was at and gave it a full rotation.

For smaller angles, for example, -1352º, you can add the biggest possible multiple of 360º, that represents the number of full rotations you have to have in order to find its first positive determination.

In this case, we found that

Satisfying the property that

Answer:

Practical Domain: 0 ≤ g ≤ 22

Practical Range: 0 ≤ C(g) ≤ 78.32

Step-by-step explanation:

The domain is the input of the function, usually, x, but it is g in this problem.

The input here is the number of gallons you can get. The tank holds a maximum of 22 gallons, so if the tank is already full, you will get 0 gallons. If the tank is completely empty, you can get up to 22 gallons. The domain is the values of the input of the function. Since the input is from 0 gallons to 22 gallons, we get this for the domain:

Practical Domain: 0 ≤ g ≤ 22

The range is the output of the function. Usually it is f(x), but in this problem it is C(g). When you input the number of gallons into the function, the output is the cost of that number of gallons. The domain is from 0 to 22 gallons. Now we use the function to find the cost of 0 gallons and the cost of 22 gallons.

Here is the function:

C(g) = 3.56g

What is the cost of 0 gallons? In this case, g = 0.

C(0) = 3.56(0) = 3.56 × 0 = 0

0 gallons cot 0 dollars, which makes sense.

What is the cost of 22 gallons, the greatest amount of fuel you can fit in the tank?

C(g) = 3.56g

Here, g = 22.

C(22) = 3.56(22) = 3.56 × 22 = 78.32

22 gallons cost 78.32 dollars.

The range of the function is from 0 dollars to 78.32 dollars.

Practical Range: 0 ≤ C(g) ≤ 78.32

We have to simplify the ratios to make them comparable;

If the ratio of green to yellow marbles is 2 to 5 and

The ratio of yellow to orange marbles is 3 to 4.

Now we can rewrite the ratios of green: yellow : orange as

From this, we can see that the ratio of green to orange marbles is;

Therefore, the ratio of green to orange marbles is 3 : 10

Answer:

6. 4

7. 8.25

Step-by-step explanation:

all the explanation for both questions is in the pics below please check it out also I am sorry if it's wrong I am only in middle school

Have a wonderful day:)

Answer:

Domain: [tex](-\infty, \infty)[/tex]

Range: [tex][0, \infty)[/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.

The Domain of the function is [ -8, 2].

The Domain of the function is [ -8, 2].

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Answer

Options A, C and D are all correct.

They simplify to give 5x - 3y

Explanation

We are asked to pick the expressions which simplify to give 5x - 3y

Taking the statements one at a time,

Option A

5x + -8y + 5y

= 5x - 8y + 5y

= 5x - 3y

This option is correct.

Option B

15xy ≠ (5x - 3y)

This option is not correct.

Option C

5 (x + y) + -8y

= 5x + 5y - 8y

= 5x - 3y

This option is correct.

Option D

-2 (2y - x) + x + x + x + y

= -4y + 2x + 3x + y

= 5x - 3y

This option is correct.

Hope this Helps!!!

Solution

For this case the correct formula for the circumference of a circle is given by:

Then the best option would be:

C = pi d

Let's first get the value of x, since it's a right triangle, we use Pythagorean Theorem.

Let's make,

a = 14.2

b = 15.5

c = x

Let's try choice c if the inequality fits,

The inequality fits, therefore c is the correct answer.

Answer:

Step-by-step explanation:

HCF of 42,72 and 90

=6

LCM of 42,72 and 90

=2520

2520 x 6 = 15120

=15120

Ok, so

We know that the annual per capita consumption of eggs was 496, and it dropped to 255.

So, We need to find the fraction eggs the average person eats in the first year as the average person did in the last year. We are given, per capital consumption of eggs in the first year = 496 and, per capital consumption of eggs in the last year = 255.

Then, earlier year had 496 eggs.

More recent year had 255 eggs.

We can say that in more recent year, the average person ate 0.5 as many eggs as the average person did in the earlier year.

0.5 comes from divide 255/496, that means that the average person ate 0.5 times eggs than the people who ate in the earlier year.

The slope intercept form of the equation that  passes through the point (2,6) and has a slope of -5 is y = -5x +16

Slope intercept form:

Slope intercept form equation is used to calculate the equation of a straight line, for the given slope of the line and intercept.

The general form of slope intercept equation is,

y = mx +c

where

m represents the slope of the line

c represents the intercept.

Given

Here we have the the point (2,6) and has a slope of -5.

Now we need to find the equation of the line for this point and slope.

While we apply these value on the formula, in order to get the value of y intercept,

Then it can look like,

6 = (-5)2 + c

6 = -10 + c

c = 6 + 10

c = 16.

Therefore, the value of y intercept is 16.

Then the equation of the line is

y = -5x + 16

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Answer:

60%

Step-by-step explanation:

Given the expression:

20 + 22 + 24 + ..... + 36

Let's write in summation notation.

Summation notation can be said to be the addition of a sequance of numbers.

From the sequence, we have:

Common difference = 22 - 20 = 2

Number of terms = 9

Apply the formula:

Where:

n = upper limit (number of terms)

i = 1 ==> lower limit

Initial value, a = 20

d = common difference = 2

To write in summation notation, we have:

ANSWER:

Based on the data given:

400 games were sold after 11 months

800 games were sold after 21 months

1500 games were sold after 36 months

We need to plot a graph of months against the number of games:

From the graph,

Yes, a single linear model is a reasonable option for the data

The equation of the graph is given by:

Note that y represents the number of months and x represents the number of board games.

The number of board games sold after 48months simply means that y= 48. In order to get x, we substitute y = 48 into the model

Therefore, the estimated number of games sold after 48 months is 2020.

The length of the ramp from the doorway is 11.94ft

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry.

To solve this problem, we are going to look at SOHCAHTOA and see which of the ratios fit in this problem.

Using Tangent of an angle, we can find the length of the ramp.

[tex]tan\theta = \frac{opposite}{adjacent}[/tex]

Let's substitute the values into the equation and solve.

[tex]tan 37 = \frac{9}{x} \\x = 11.94ft[/tex]

The length of the ramp is 11.94ft

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Solution

For this case we have the following:

1/2 s = 7/2

We can multiply both sides by 2 and we got:

s = 7

If a particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams and I pick 9 fruits at random, then their mean weight will be greater than 605.29263 grams 16% of the time.

As per the question statement, a particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams and I pick 9 fruits at random.

We are required to calculate their mean weight will be greater than how many grams for 16% of the time.

Given (μ = 598), (σ = 22), and (n = 9)

Therefore, the standard deviation of the distribution of sample, otherwise know as the standard error, will be [s = (sdp)/√(ss)]

Where, "s" is the standard error, "sdp" is the standard deviation of the population and "ss" is the sample size.

Therefore, [s = (22/√9) = (22/3) = 7.33...

Now, we need to look up the z-score for an area to the right of it being equal to (0.16) since we are concerned about (16%) times among the random selection, and [16% = (16/100) = 0.16]

That is, we need to look up the z-score for an area of [(1 - 0.16) = 0.84] to the left of it.

Hence, a z-score with an area of 0.84 to the left of it will be equal to 0.99445.

Now to find the raw score associated with this, we will have to use the formula to calculate z-score which goes as [(x - m)/s].

Where, "z" is the z-score, "x" is the raw score, "m" is the mean and "s" is the standard error.

Therefore, with a mean of 598 and a standard error of 7.333 and a z-score of 0.99445, applied to the above mentioned formula to calculate z-score, we get:

[0.99445 = (x - 598)/7.33]

Or, (x - 598) = (0.99445 * 7.33)

Or, (x - 598) = 7.29263

Or, x = (598 + 7.29263)

Or, [x = 605.29263]

That is, if I pick a sample of 9 fruits at random, then their mean weight will be greater than 605.29263 grams 16% of the time.

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1. The total earnings of the paralegal from this job was £4,680.

2. The amount of the earnings allocated to her savings, based on the allocation ratio, is £2,808.

The total earnings are a function of the unit hours worked and the hourly pay rate.

The total earnings are the product of the multiplication of the two variables.

A ratio is a numerical relationship showing how much a value is contained in another value or variable.

Ratios are fractional values depicted in percentages, decimals, or fractions.

The total number of work hours = 19.5 hours

The work hour rate (per hour) = £240

The total earnings from the job = £4,680 (£240 x 19.5)

The ratio of utilities and savings = 2:3

The sum of the ratio = 5

The amount allocated to savings = 3/5 of £4,680 = £2,808.

The amount allocated to utilities = £1,872 or 2/5 (£4,680 - £2,808)

Thus, whereas, the paralegal earned £4,680 from the job, the amount allocated to her savings is £2,808, based on the subsisting allocation ratio.

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Given:

Point; (x, y) ==> (2, 5)

Slope, m = 2

To write a linear equation that goes through the point, apply the slop-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

Take the following steps:

• Step 1:

Substitute 2 for m.

Input the points (2, 5) for the values of x and y repsectively

y = mx + b

5 = 2(2) + b

5 = 4 + b

• Step 2:

Solve for b.

Subtract 4 from both sides

5 - 4 = 4 - 4 + b

1 = b

Therefore, to write the linear equation, substitute 2 for m, and 1 for b in (y = mx + b)

y = mx + b

y = 2x + 1

Therefore, the equation for the line that goes through the point (2, 5) and has a slope of 2 is:

y = 2x + 1

ANSWER:

Answer:

The function A is given below as

Using a graphing tool, we will have the graph be

Hence,

Equation A matches graph 3 because the x-intercepts are on the positive x-axis and it has a y-intercept of 8(on the positive y-axis)

Step 2:

Equation B is given below as

Using the graphing tool, we will have the graph as

Hence,

Equation B matches graph 4

The x-intercepts cuts at the negative x and positive x-axis and the y-intercepts is on the negative y-axis

Step 3:

Equation C is given below as

Hence,

Using a graphing calculator, we will have the graph as

Hence,

Equation C matches Graph 1, because its vertex is (6,8) and it has a y-intercept on the positive y-axis

Answer:

62.5 mph

Step-by-step explanation:

rate * time = distance

50 * 3 = 150 mi

70 * 5 = 350 mi

total miles = 500 mi

 total time = 8 hrs

Average = 500 mi / 8hr = 62.5 mi / hr

we must first find the price of labor

then we subtract the value of the parts from the total

the price of the labor was 98$

now to calculate the percent, divide the price of the labor between the total and multiply by 100

the percent was 70%

Part A. To find the growth factor of the town, you can proceed like this

So, the growth factor for the town will be

For part B, exponential growth is modeled by the equation

So, you have

For part C, you need to find the population in 2011, so

Then, plug in the equation found x = 5

Therefore, the population of Tewksbury in 2011 will be 27874 people.

The number (2x)(3x) in the word will be two time the variable multiplied the three times the variable.

For the given question,

The number in digits is given as (2x)(3x).

The 'x' is the variable part who value is not defined for the question.

Thus, twice the variable will be 2x.

Thrice the variable will be 3x.

The multiplication of both the numbers will be  (2x)(3x).

Therefore, in words the number will be written as two time the variable multiplied the three times the variable.

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Answer:

  D.  (4, -12)

Step-by-step explanation:

Given the equation of a circle is (x -4)² +(y +12)² = 17², you want to know the center.

The equation of a circle centered at (h, k) with radius r is ...

  (x -h)² +(y -k)² = r²

Comparing this to the given equation, we can identify the values of the parameters as ...

  (x -4)² +(y +12)² = 17²

  h = 4, -k = 12, r = 17 . . . . . k = -12

This tells us the center is ...

  (h, k) = (4, -12) . . . . . matches choice D

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6x² = x + 2

Subtracting x and 2 at both sides:

6x² - x - 2 = x + 2 - x - 2

6x² - x - 2 = 0

where

a: 6

b: -1

c: -2

Substituting these values into the quadratic formula:

Here, the given function is f(x)=c.

Check whether the function is odd or even.

Here, the out put of the function is constant whether it is +x or -x.

So, the function is even.

The graph of the function f(x)=c is shown below.

From, the graph, for any values of x there is a constant val;ue of y.

The function is symmetric with respect to y axis.

The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.

According to the question,

We have to divide 430 by 8 by following the long division method.

Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.

Now, we will solve it step by step.

In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.

So, we have a = 5, b = 4 and c = 0.

Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.

So, we have d = 3.

Now, when we will subtract 24 from 30, we will get 6.

So, we have e = 6.

And e is also the remainder, R. So, we have R = 6.

Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.

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